This project studies different types of chemical and medical instrumentation with the aim of designing experiments that are optimal with respect to specified criteria. Considerable effort has been put into the optimization of NMR experiments both for measuring spin-lattice relaxation times (T1) and reaction rates in physiological systems. The first of these finds wide use in both medical imaging and chemical measurements, while the second gives important physiological data which can be measured in vivo. In the design of T1 experimented an optimal two-stage measurement has been developed in which the first stage is used to give a rough estimate of this parameter and the second stage is used to refine the estimate. A joint experimental and theoretical investigation of the effects of noise in x-ray crystallography has shown that the customary assumption of Poisson noise is only valid under specific experimental conditions. A more accurate estimate of the noise distribution has been suggested based on data collected at Tel-Aviv University.